In our approach to assess long-term nutrient input requirements it is postulated that the annual application rates of macro-nutrients (N, P, K) should at least be equal to total nutrient uptake in the aboveground crop biomass (grain and stover) at a given target yield, YT. In this way, the minimum input requirements (A, kgnutrient ha-1) are equivalent to the uptake requirements (U, kgnutrient ha-1) of the crop at the target yield.

The nutrient uptake for a given YT is calculated using selected principles of the QUEFTS model (Janssen et al., 1990). These include (1) a coefficient to express physiological efficiency of each nutrient (kg grain per kg uptake of the nutrient in total crop biomass) (Table 1 – we used medium values); (2) balanced nutrition implying that overall efficiency is best served if the different nutrients are taken up in optimum stoichiometric ratios to one another; (3) both physiological efficiency and nutrient uptake ratios (N/P/K) are constant up to a given relative target yield (YT/Yw), here 0.62; and (4) beyond this point the N-use efficiency decreases non-linearly as the target yield approaches the yield ceiling Yw as a result of extra nutrient uptake. This decline is defined by linear decreases of both derivatives dY/dU and dU/dA from their initial values (valid up to YT/Yw=0.62) to zero at the yield ceiling (YT=Yw). In contrast to N, the physiological efficiency of which decreases for YT/Yw exceeding 0.62, no accumulation of P or K in crop biomass is presumed beyond the 62% point, and therefore the input requirements of P and K are constant per kg grain produced.

The above implies a course of agronomic N use efficiency (N-AE, kg grain per kg nutrient applied) versus relative yield that starts at 52 kg kg-1 which is maintained for yields up to 62% of Yw, and then declines to reach ca. 46 kg kg-1 for yields representing 80% of Yw. Yields are expressed at 15.5% moisture. (This corresponds to N-AE = 50 kg kg-1 at 12% moisture, which implies that 20 kg of N input is needed per ton of maize grain produced.)

This approach to minimum nutrient input requirement assumes that other management factors are optimal so as to avoid yield limitations other than due to water (in rainfed conditions), while yield reducing factors (weeds, pests and diseases) are well-controlled.

In a steady-state equilibrium (soil nutrient pools are constant) the annual nutrient losses are – by definition - equal to the difference between nutrient input and offtake, i.e. to the nutrient surplus. This means that in crops where only the grains are harvested and all crop residues are retained on the field, the postulated condition (input equals uptake in aboveground biomass) implies that the annual nutrient loss is equal to the amount of the nutrient contained in crop residues. This approach is suitable for long-term calculations where soil nutrient pools adapt to a given input regime.

One may argue that these minimum N input requirements are a very optimistic (i.e., ‘low') estimate of actual N input requirements. This is certainly true for a system where all residues are harvested, as our approach then implies that all added fertiliser N is either taken up by the crop or substitutes N taken up from the soil pool, at any ratio between these two. That implies zero N losses via volatilisation (NH3), denitrification (N2 and N2O), or leaching (nitrate). In contrast, for a system where all residues are returned to the soil, the proposed minimum N input requirement implies that annual N losses are equivalent to the amount of N in the stover, and this may be achievable for N provided highly efficient management. For P and K the crop-soil system is less ‘leaky' than for N, and sustaining target yields at the stated minimum input requirements will be easier, except on P-fixing soils. In summary, our minimum N,P,K requirements can be seen as a well-defined target, presuming highly efficient management, no soil mining of nutrients and low losses to the environment. The given values indicate the minimum amounts of macro-nutrients that are likely needed on the longer term to achieve a defined target yield. When using the minimum input requirements, it should be born in mind that currently, actual agronomic nutrient efficiencies might be much lower due to sub-optimal management, and therefore nutrient losses to the environmental also higher than implicated here.

For a more comprehensive description of quantifying minimum nutrient input requirements and balanced nutrition, see Ten Berge et al., 2019.

*These parameters are consistent with those of http://www.ipni.net/article/IPNI-3346. For other examples of analyses of yield-uptake relationships or the use of balanced nutrition, see e.g. Witt et al. (1999) for rice and Setiyono et al. (2011) for maize.

Ockerby, S.E., Adkins, S.W. and Garside, A.L., 1999. The uptake and use of nitrogen by paddy rice in fallow, cereal, and legume cropping systems. Australian Journal of Agricultural Research, 50(6): 945-952.